PPT
... Subset sum problem • The reduction to show Subset Sum is NPcomplete involves numbers with n digits • In that case, the O(nW) algorithm is an exponential time and space algorithm ...
... Subset sum problem • The reduction to show Subset Sum is NPcomplete involves numbers with n digits • In that case, the O(nW) algorithm is an exponential time and space algorithm ...
CS 315: Computer Logic and Digital Design
... 2 until the quotient is 0. The remainders form the answer, with the first remainder as the least significant bit (LSB) and the last as the most significant bit (MSB). ...
... 2 until the quotient is 0. The remainders form the answer, with the first remainder as the least significant bit (LSB) and the last as the most significant bit (MSB). ...
The hailstone sequence
... As of 2012, the Collatz conjecture is unproven. There is a research paper that comes close, but unfortunately contains some incomplete reasoning: http://preprint.math.uni-hamburg.de/public/papers/hbam/hbam2011-09.pdf ...
... As of 2012, the Collatz conjecture is unproven. There is a research paper that comes close, but unfortunately contains some incomplete reasoning: http://preprint.math.uni-hamburg.de/public/papers/hbam/hbam2011-09.pdf ...
CMP3 Glossary - Connected Mathematics Project
... decay factor The constant factor that each value in an exponential decay pattern is multiplied by to get the next value. The decay factor is the base in an exponential decay equation, and is a number between 0 and 1. For example, in the equation A = 64(0.5)n, where A is the area of a ballot and n is ...
... decay factor The constant factor that each value in an exponential decay pattern is multiplied by to get the next value. The decay factor is the base in an exponential decay equation, and is a number between 0 and 1. For example, in the equation A = 64(0.5)n, where A is the area of a ballot and n is ...
Some Useful Properties of Complex Numbers Complex numbers
... The next step is to try to make use of the formulae Eq. (8) and Eq. (9) given above for sin and cos. To do this we ‘extract’ a factor exp(−iN δ/2) from the numerator and exp(−iδ/2) from the denominator of the fraction appearing in Eq. (15) which produces the result: ...
... The next step is to try to make use of the formulae Eq. (8) and Eq. (9) given above for sin and cos. To do this we ‘extract’ a factor exp(−iN δ/2) from the numerator and exp(−iδ/2) from the denominator of the fraction appearing in Eq. (15) which produces the result: ...
PowerPoint - Balancing Equations Using Oxidation
... 3. Identify which atoms change oxidation number 4. Make the number of atoms that change oxidation number the same on both sides by inserting temporary coefficients 5. Compute the total change in oxidation number 6. Make the total increase in oxidation number equal the total decrease by multiplicatio ...
... 3. Identify which atoms change oxidation number 4. Make the number of atoms that change oxidation number the same on both sides by inserting temporary coefficients 5. Compute the total change in oxidation number 6. Make the total increase in oxidation number equal the total decrease by multiplicatio ...
2007 Mathematical Olympiad Summer Program Tests
... 2.1. Let {an }∞ n=1 = {2, 4, 8, 1, 3, 6, . . . } be the infinite integer sequence such that an is the leftmost digit in the decimal representation of 2n , and let {bn }∞ n=1 = {5, 2, 1, 6, 3, 1, . . . } be the infinite integer sequence such that an is the leftmost digit in the decimal representation ...
... 2.1. Let {an }∞ n=1 = {2, 4, 8, 1, 3, 6, . . . } be the infinite integer sequence such that an is the leftmost digit in the decimal representation of 2n , and let {bn }∞ n=1 = {5, 2, 1, 6, 3, 1, . . . } be the infinite integer sequence such that an is the leftmost digit in the decimal representation ...
Addition
Addition (often signified by the plus symbol ""+"") is one of the four elementary, mathematical operations of arithmetic, with the others being subtraction, multiplication and division.The addition of two whole numbers is the total amount of those quantities combined. For example, in the picture on the right, there is a combination of three apples and two apples together; making a total of 5 apples. This observation is equivalent to the mathematical expression ""3 + 2 = 5"" i.e., ""3 add 2 is equal to 5"".Besides counting fruits, addition can also represent combining other physical objects. Using systematic generalizations, addition can also be defined on more abstract quantities, such as integers, rational numbers, real numbers and complex numbers and other abstract objects such as vectors and matrices.In arithmetic, rules for addition involving fractions and negative numbers have been devised amongst others. In algebra, addition is studied more abstractly.Addition has several important properties. It is commutative, meaning that order does not matter, and it is associative, meaning that when one adds more than two numbers, the order in which addition is performed does not matter (see Summation). Repeated addition of 1 is the same as counting; addition of 0 does not change a number. Addition also obeys predictable rules concerning related operations such as subtraction and multiplication.Performing addition is one of the simplest numerical tasks. Addition of very small numbers is accessible to toddlers; the most basic task, 1 + 1, can be performed by infants as young as five months and even some non-human animals. In primary education, students are taught to add numbers in the decimal system, starting with single digits and progressively tackling more difficult problems. Mechanical aids range from the ancient abacus to the modern computer, where research on the most efficient implementations of addition continues to this day.